'high-up' definitions:

Definition of 'high-up'

From: WordNet
noun
An important or influential (and often overbearing) person [syn: very important person, VIP, high-up, dignitary, panjandrum, high muckamuck]

Definition of 'high-up'

From: GCIDE
  • high-up \high-up\ n. an important or influential person.
  • Syn: very important person, VIP, dignitary, panjandrum. [WordNet 1.5]